Please help me w/ this finance math problem: time to pay off a $125000 mortgage?

[davidtrinh]

How long does it take to pay off a $125000 mortgage if the annual interest rate is 5.5% and compounded monthly with a monthly payment of $710?

Below is my attempt.

I use the formula

FV = P* ((1+r/n)^(nt)-1)/(r/n)

where FV is future value, r is the interest rate, n is the number of compounding periods in a year, t is the elapsed time, and P is the principal.

12500 = 710*((1+0.055/12)^(12t)-1)/(0.055/12)

Next, I divide both sides by 710 and then multiply both 0.055/12.

3841.24 = (1.0045833333)^(12t)

Then, I take the log of both sides.

log3841.24 = 12t*log1.004583

Lastly, I solve for t and get t = 150 years.

But, the answer key says 30 years.

Can someone explain how to do the problem? Thanks a lot.

 

[JeffM]

How long does it take to pay off a $125000 mortgage if the annual interest rate is 5.5% and compounded monthly with a monthly payment of $710?

Below is my attempt.

I use the formula

FV = P* ((1+r/n)^(nt)-1)/(r/n)

where FV is future value, r is the interest rate, n is the number of compounding periods in a year, t is the elapsed time, and P is the principal.

12500 = 710*((1+0.055/12)^(12t)-1)/(0.055/12)

Next, I divide both sides by 710 and then multiply both 0.055/12.

3841.24 = (1.0045833333)^(12t)

Then, I take the log of both sides.

log3841.24 = 12t*log1.004583

Lastly, I solve for t and get t = 150 years.

But, the answer key says 30 years.

Can someone explain how to do the problem? Thanks a lot.

Like Denis, I am baffled. I can't even follow your arithmetic.

\(\displaystyle \dfrac{125000}{710} * \dfrac{0.055}{12} \approx 0.807 << 3841.24.\)

But why are you bothering with future value? The present value of the payments to be made in the future must equal the current value of the mortgage amount.